The principal aim of this research proposal is to continue the analytical work that has been initiated on the characteristics of iterative image reconstruction algorithms for tomography and to apply the results of the research to the design and implementation algorithms that provide significant improvements in image quality over the customary filtered backprojection methods used currently. By having studied the unmodified MLE algorithm in detail, we have attained a substantial degree of understanding of what the role of target functions to be maximized or minimized is in iterative schemes. In particular, we have discovered the need for a stopping rule to prevent the iterative process to proceed into a region of solutions that are in contradiction with the fundamental Poisson nature of projection data and we have proposed such a rule. We now propose to continue analytical research of a similar nature with other algorithms that are being considered for iterative reconstruction with the aim of building a base of knowledge from which we can design new target functions and their algorithms to make the best use of the projection data with highest statistical significance. We also propose carrying out an ROC test of the new algorithms in collaboration with the Dept. of Radiological Sciences, UCLA, for the purpose of proving the value of the new algorithms. As a long range objective, we intend to bring into the algorithms design process the knowledge of the developing field of perception of Psychophysics as a way to insure that future developments in algorithms are not longer based on more or less successful intuitive ideas of what a radiologist should perceive when observing a medical tomographic image.